Feedback can increase the degrees of freedom of the rank-deficient interference channel

We characterize the total degrees of freedom (DoF) of the two-user rank-deficient interference channel with feedback, in which transmitter i and receiver j use M_i and N_j antennas, respectively, and the rank of the channel matrix between transmitter i and receiver j is given by D_ji ≤ min(M_i, N_j) ∀i, j = 1,2. One consequence of this result is that feedback can increase the DoF when the number of antennas at each node is large enough as compared to the ranks of channel matrices. This finding is in contrast to the full-rank interference channel where feedback provides no DoF gain. The gain comes from using feedback to provide alternative signal paths, thereby effectively increasing the ranks of desired channel matrices.